THERMAL APPLICATIONS NOTE Polymer Heats of Fusion

Total Page：16

File Type：pdf, Size：1020Kb

THERMAL APPLICATIONS NOTE Polymer Heats of Fusion Roger L. Blaine TA Instruments,109 Lukens Drive, New Castle DE 19720, USA The heat of fusion of 100 % crystalline polymer is required to obtain percent crystallinity by differential scanning calorimetry (1). Polymer reference materials with 100 % crystallinity are rarely available for comparison purposes. Fortunately, the heats of fusion values for 100 % crystalline polymers may be determined by indirect methods such as extrapolation using the Flory equation (2). Wunderlich and co-workers (3) have created tables of best estimate values for the heats of fusion for a wide variety of linear polymers with values reported in joules per mole of repeat unit. To be useful for thermal analysis purposes, these enthalpy values need to be normalized to mass. Table 1 includes the mass normalized enthalpy of fusion values commonly used in DSC determinations. REFERENCES 1. TA123, “Determination of Polymer Crystallinity by DSC”, TA Instruments, New Castle, DE. 2. TA276, “Determination of Polymer Crystal Molecular Weight Distribution by DSC”, TA Instruments, New Castle, DE. 3. B. Wunderlich, Thermal Analysis, Academic Press, 1990, pp. 417-431. 4. D1600, “Abbreviated Terms Relating to Plastics”, American Society for Testing and Materials, West Conshohocken, PA. KEYWORDS differential scanning calorimetry, melting, thermoplastic polymers 1 TN048 Table 1 – Polymer Heats of Fusion Acronym Name Enthalpy Repeat Unit Molecular Enthalpy (4) (kJ/mol) Weight (J/g) (3) (g/mol) PE Polyethylene 4.11 -CH2- 14.03 293 PP Polypropylene 8.70 -CH2CH(CH3)- 42.08 207 PB Polybutene-1 7.00 -CH2CH(C2H5) 56.1 125 POM Polymethylenoxide 9.79 -CH2O- 30.03 326 PEOX Polyethyleneoxide 8.66 -CH2CH2O- 44.05 197 PA6 Polycaprolactam 26.0 -NH(CH2)5CO- 113.2 230 PA11 Polyundecanolactam 44.7 -NH(CH2)10CO- 183.3 244 PA12 Polylauryllactam 48.4 -NH(CH2)11CO- 197.3 245 PA66 Poly(hexamethylene adipamide) 57.8 -NH(CH2)6NHCO(CH2)4CO- 256.3 226 PA69 Poly(hexamethylene nonanediamide) 69 -NH(CH2)6NHCO(CH2)7CO- 268.4 257 PA610 Poly(hexamethylene sebacamide) 71.7 -NH(CH2)6NHCO(CH2)8CO- 282.4 254 PA612 Poly(hexamethylene dodecanediamide) 80.1 -NH(CH2)6NHCO(CH2)10CO- 310.5 258 PVOH Polyvinyl alcohol 7.11 -CH2CH(OH)- 44.05 161 PET Polyethylene terephathalate 26.9 -O(CH2)2O2CC6H4CO- 192.2 140 PBT Polybutylene terephathalate 32.0 -O(CH2)4O2CC6H4CO- 220.2 145 PVF Polyvinyl fluoride 7.54 -CH2CH(F)- 46.04 164 PVDF Polyvinylidene fluoride 6.70 -CH2CF2- 64.03 105 Polytrifluoroethylene 5.44 -CH(F)CF2- 82.0 66.3 PTFE Polytetrafluoroethylene 4.10 -CF2- 50.0 82.0 PVC Polyvinyl chloride 11.0 -CH2CH(Cl)- 62.50 176 PCTFE Polychlorotrifluoroethylene 5.02 -CF2CF(Cl)- 116.5 43.1 PEEK Polyetheretherketone 37.4 -C6H4COC6H4OC6H4O- 288.3 130 2 TN048.

Copy Link

Recommended publications

High Temperature Enthalpies of the Lead Halides
HIGH TEMPERATURE ENTHALPIES OF THE LEAD HALIDES: ENTHALPIES AND ENTROPIES OF FUSION APPROVED: Graduate Committee: Major Professor Committee Member Min fessor Committee Member X Committee Member UJ. Committee Member Committee Member Chairman of the Department of Chemistry Dean or the Graduate School HIGH TEMPERATURE ENTHALPIES OF THE LEAD HALIDES: ENTHALPIES AND ENTROPIES OF FUSION DISSERTATION Presented to the Graduate Council of the North Texas State University in Partial Fulfillment of the Requirements For the Degree of DOCTOR OF PHILOSOPHY By Clarence W, Linsey, B. S., M. S, Denton, Texas June, 1970 ACKNOWLEDGEMENT This dissertation is based on research conducted at the Oak Ridge National Laboratory, Oak Ridge, Tennessee, which is operated by the Uniofl Carbide Corporation for the U. S. Atomic Energy Commission. The author is also indebted to the Oak Ridge Associated Universities for the Oak Ridge Graduate Fellowship which he held during the laboratory phase. 11 TABLE OF CONTENTS Page LIST OF TABLES iv LIST OF ILLUSTRATIONS v Chapter I. INTRODUCTION . 1 Lead Fluoride Lead Chloride Lead Bromide Lead Iodide II. EXPERIMENTAL 11 Reagents Fusion-Filtration Method Encapsulation of Samples Equipment and Procedure Bunsen Ice Calorimeter Computer Programs Shomate Method Treatment of Data Near the Melting Point Solution Calorimeter Heat of Solution Calculations III. RESULTS AND DISCUSSION 41 Lead Fluoride Variation in Heat Contents of the Nichrome V Capsules Lead Chloride Lead Bromide Lead Iodide Summary BIBLIOGRAPHY ...... 98 in LIST OF TABLES Table Pa8e I. High-Temperature Enthalpy Data for Cubic PbE2 Encapsulated in Gold 42 II. High-Temperature Enthalpy Data for Cubic PbF2 Encapsulated in Molybdenum 48 III.
[Show full text]
Polymer Dynamics
Polymer Dynamics 2017 School on Soft Matters and Biophysics Instructor: Alexei P. Sokolov, e-mail: [email protected] Text: Instructor's notes with supplemental reading from current texts and journal articles. Please, have the notes printed out before each lecture. Books (optional): M.Doi, S.F.Edwards, “The Theory of Polymer Dynamics”. Y.Grosberg, A.Khokhlov, “Statistical Physics of Macromolecules”. J.Higgins, H.Benoit, “Polymers and Neutron Scattering”. 1 Course Content: I. Introduction II. Experimental methods for analysis of molecular motions III. Vibrations IV. Fast and Secondary Relaxations V. Segmental Dynamics and Glass Transition VI. Chain Dynamics and Viscoelastic Properties VII. Rubber Elasticity VIII. Concluding Remarks 2 INTRODUCTION Polymers are actively used in many technologies Traditional technologies: Even better perspectives for use in novel technologies: Example: Light-weight materials Boeing-787 “Dreamliner” 80% by volume is plastic Materials for energy generation Example: polymer solar cells Materials for energy storage Example: Polymer-based Li battery Polymers have huge potential for applications in Bio-medical field “Smart” materials, stimuli-responsive, self-healing … 3 Polymers Polymers are long molecules They are constructed by covalently bonded structural units – monomers Main difference between properties of small molecules and polymers is related to the chain connectivity Advantages of Polymeric Based Materials: Easy processing, relatively cheap manufacturing Light weight (contain mostly light elements like C, H, O) Unique viscoelastic properties (e.g. rubber elasticity) Extremely broad tunability of macroscopic properties 4 Definitions o Monomer – repeat unit, structural block of the polymer chain o Oligomer – short chains, ~ 3-10 monomers o Polymers – long chains, usually hundreds of monomers o Degree of polymerization – number of monomers in the polymer chain Molecular weight: Weight of the molecule M [g/mol].
[Show full text]
Chapter 11 Liquids, Solids, and Phase Changes
Lecture Presentation Chapter 11 Liquids, Solids, and Phase Changes 11.1, 11.2, 11.3, 11.4, 11.15, 11.17, 11.26, 11.30, 11.32, 11.40, 11.42, 11.60, 11.82, 11.116 John E. McMurry Robert C. Fay Properties of Liquids Viscosity: The measure of a liquid’s resistance to flow (higher intermolecular force, higher viscosity) Surface Tension: The resistance of a liquid to spread out and increase its surface area (forms beads) (higher intermolecular force, higher surface tension) Properties of Liquids low intermolecular force – low viscosity, low surface tension high intermolecular force – high viscosity, high surface tension HW 11.1 Properties of Liquids high intermolecular force – high viscosity, high surface tension For the following molecules which has the higher intermolecular force, viscosity and surface tension ? (LD structure, VSEPRT, dipole of molecule) (if the molecules are in the liquid state) a. CHCl3 vs CH4 b. H2O vs H2 (changed from handout) c. N Cl3 vs N H Cl2 Phase Changes between Solids, Liquids, and Gases Phase Change (State Change): A change in the physical state but not the chemical identity of a substance Fusion (melting): solid to liquid Freezing: liquid to solid Vaporization: liquid to gas Condensation: gas to liquid Sublimation: solid to gas Deposition: gas to solid Phase Changes between Solids, Liquids, and Gases Enthalpy – add heat to system Entropy – add randomness to system Phase Changes between Solids, Liquids, and Gases Heat (Enthalpy) of Fusion (DHfusion ): The amount of energy required to overcome enough intermolecular forces to convert a solid to a liquid Heat (Enthalpy) of Vaporization (DHvap): The amount of energy required to overcome enough intermolecular forces to convert a liquid to a gas HW 11.2: Phase Changes between Solids, Liquids, & Gases DHfusion solid to a liquid DHvap liquid to a gas At phase change (melting, boiling, etc) : DG = DH – TDS & D G = zero (bc 2 phases in equilibrium) DH = TDS o a.
[Show full text]
Biodegradable Polymeric Biomaterials in Different Forms for Long-Acting
University of Tennessee Health Science Center UTHSC Digital Commons Theses and Dissertations (ETD) College of Graduate Health Sciences 5-2017 Biodegradable Polymeric Biomaterials in Different Forms for Long-acting Contraception and Drug Delivery to the Eye and Brain Dileep Reddy Janagam University of Tennessee Health Science Center Follow this and additional works at: https://dc.uthsc.edu/dissertations Part of the Pharmaceutics and Drug Design Commons Recommended Citation Janagam, Dileep Reddy (http://orcid.org/0000-0002-7235-7709), "Biodegradable Polymeric Biomaterials in Different Forms for Long-acting Contraception and Drug Delivery to the Eye and Brain" (2017). Theses and Dissertations (ETD). Paper 425. http://dx.doi.org/10.21007/etd.cghs.2017.0429. This Dissertation is brought to you for free and open access by the College of Graduate Health Sciences at UTHSC Digital Commons. It has been accepted for inclusion in Theses and Dissertations (ETD) by an authorized administrator of UTHSC Digital Commons. For more information, please contact [email protected]. Biodegradable Polymeric Biomaterials in Different Forms for Long-acting Contraception and Drug Delivery to the Eye and Brain Document Type Dissertation Degree Name Doctor of Philosophy (PhD) Program Pharmaceutical Sciences Track Pharmaceutics Research Advisor Tao L. Lowe, Ph.D. Committee Joel Bumgardner, Ph.D. James R. Johnson, Ph.D. Bernd Meibohm, Ph.D. Duane D. Miller, Ph.D. ORCID http://orcid.org/0000-0002-7235-7709 DOI 10.21007/etd.cghs.2017.0429 Comments Two year embargo expires
[Show full text]
Cryometric Determination of the Enthalpy of Fusion of Sodium Cryolite
Cryometric determination of the enthalpy of fusion of sodium cryolite M. MALINOVSKÝ Department of Chemical Technology of Inorganic Substances, Slovak Technical University, CS-812 37Bratislava Received 30 July 1982 Accepted for publication 22 August 1983 Using the method of classical thermal analysis a part of the liquidus of sodium cryolite in the system Na3AlF6—Na3FS04 was measured in the compo sition range 0—5 mole % Na3FS04. On the basis of these results the molar enthalpy of fusion of cryolite was calculated. It was found that AHf(Na3AlFft) = = 115.4 kJ mol"1; error in this result was estimated to be ±4.9 %. Методом классического термического анализа измерена часть ликви дуса натриевого криолита в системе Na3AlF6—Na3FS04 в интервале кон центраций 0—5 мол. % Na3FS04. На основании этих результатов рассчи тана мольная энтальпия плавления криолита. Найдено, что 1 AH,(Na3AlF6) = 115,4 кДж моль" ; точность этого результата ±4,9 %. Literature survey and theoretical Knowledge of the enthalpy of fusion of sodium hexafluoroaluminate Na3AlF6 (cryolite) is important both from theoretical and practical points of view. For example, it is needed at calculation of the thermal and energy balance and/or the thermal inertia of aluminium cells (the electrolyte contains about 90 mass % of Na3AlF6). The most precise values of the molar enthalpy of fusion AHf(i) of chemical substances can be generally obtained from calorimetric measurements. However, when we deal with substances having higher melting temperature and which are also unstable and very corrosive the calorimetric determination of the quantity AHf(i) can be less reliable. In the case of cryolite Roth and Bertram [1] found from the calorimetric 1 1 measurements ÄH,(Na3 A1F6) = 16.64 kcal mol" = 69.62 kJ mol" .
[Show full text]
Thermodynamic Temperature
Thermodynamic temperature Thermodynamic temperature is the absolute measure 1 Overview of temperature and is one of the principal parameters of thermodynamics. Temperature is a measure of the random submicroscopic Thermodynamic temperature is defined by the third law motions and vibrations of the particle constituents of of thermodynamics in which the theoretically lowest tem- matter. These motions comprise the internal energy of perature is the null or zero point. At this point, absolute a substance. More specifically, the thermodynamic tem- zero, the particle constituents of matter have minimal perature of any bulk quantity of matter is the measure motion and can become no colder.[1][2] In the quantum- of the average kinetic energy per classical (i.e., non- mechanical description, matter at absolute zero is in its quantum) degree of freedom of its constituent particles. ground state, which is its state of lowest energy. Thermo- “Translational motions” are almost always in the classical dynamic temperature is often also called absolute tem- regime. Translational motions are ordinary, whole-body perature, for two reasons: one, proposed by Kelvin, that movements in three-dimensional space in which particles it does not depend on the properties of a particular mate- move about and exchange energy in collisions. Figure 1 rial; two that it refers to an absolute zero according to the below shows translational motion in gases; Figure 4 be- properties of the ideal gas. low shows translational motion in solids. Thermodynamic temperature’s null point, absolute zero, is the temperature The International System of Units specifies a particular at which the particle constituents of matter are as close as scale for thermodynamic temperature.
[Show full text]
Lecture Notes on Structure and Properties of Engineering Polymers
Structure and Properties of Engineering Polymers Lecture: Microstructures in Polymers Nikolai V. Priezjev Textbook: Plastics: Materials and Processing (Third Edition), by A. Brent Young (Pearson, NJ, 2006). Microstructures in Polymers • Gas, liquid, and solid phases, crystalline vs. amorphous structure, viscosity • Thermal expansion and heat distortion temperature • Glass transition temperature, melting temperature, crystallization • Polymer degradation, aging phenomena • Molecular weight distribution, polydispersity index, degree of polymerization • Effects of molecular weight, dispersity, branching on mechanical properties • Melt index, shape (steric) effects Reading: Chapter 3 of Plastics: Materials and Processing by A. Brent Strong https://www.slideshare.net/NikolaiPriezjev Gas, Liquid and Solid Phases At room temperature Increasing density Solid or liquid? Pitch Drop Experiment Pitch (derivative of tar) at room T feels like solid and can be shattered by a hammer. But, the longest experiment shows that it flows! In 1927, Professor Parnell at UQ heated a sample of pitch and poured it into a glass funnel with a sealed stem. Three years were allowed for the pitch to settle, and in 1930 the sealed stem was cut. From that date on the pitch has slowly dripped out of the funnel, with seven drops falling between 1930 and 1988, at an average of one drop every eight years. However, the eight drop in 2000 and the ninth drop in 2014 both took about 13 years to fall. It turns out to be about 100 billion times more viscous than water! Pitch, before and after being hit with a hammer. http://smp.uq.edu.au/content/pitch-drop-experiment Liquid phases: polymer melt vs.
[Show full text]
Enthalpy of Sublimation in the Study of the Solid State of Organic Compounds
J. Phys. Chem. B 2005, 109, 18055-18060 18055 Enthalpy of Sublimation in the Study of the Solid State of Organic Compounds. Application to Erythritol and Threitol A. J. Lopes Jesus, Luciana I. N. Tome´, M. Ermelinda Euse´bio,* and J. S. Redinha Department of Chemistry, UniVersity of Coimbra, 3004-535, Coimbra, Portugal ReceiVed: March 30, 2005; In Final Form: July 5, 2005 The enthalpies of sublimation of erythritol and L-threitol have been determined at 298.15 K by calorimetry. The values obtained for the two diastereomers differ from one another by 17 kJ mol-1. An interpretation of these results is based on the decomposition of this thermodynamic property in a term coming from the intermolecular interactions of the molecules in the crystal (∆intH°) and another one related with the conformational change of the molecules on going from the crystal lattice to the most stable forms in the gas phase (∆confH°). This last term was calculated from the values of the enthalpy of the molecules in the gas state and of the enthalpy of the isolated molecules with the crystal conformation. Both quantities were obtained by density functional theory (DFT) calculations at the B3LYP/6-311G++(d,p) level of theory. The results obtained in this study show that the most important contribution to the differences observed in the enthalpy of sublimation are the differences in the enthalpy of conformational change (13 kJ mol-1) rather than different intermolecular forces exhibited in the solid phase. This is explained by the lower enthalpy of threitol in the gas phase relative to erythritol, which is attributed to the higher strength of the intramolecular hydrogen bonds in the former.
[Show full text]
Chemistry 531 Spring 2009 Problem Set 5 Solutions
Chemistry 531 Spring 2009 Problem Set 5 Solutions 1. For the reaction CH4(g) + 2O2(g) −→ CO2(g) + 2H2O(l) use Table 4-2 on page 50 and Table 7-2 on page 171 of your text books to determine at 25◦C (a) the amount of heat liberated per mole at constant pressure; Answer: ◦ −1 ∆rHm = [2(−285.83) + (−393.509) − (−74.81)]kJ mol = −890.359kJ mol−1 (b) the maximum amount of work obtainable per mole for the reaction; Answer: ◦ −1 −1 ∆rGm = [2(−237.129) + (−394.359) − (−50.72)]kJ mol = −817.897kJ mol A = G − pV ◦ ◦ ∆rAm = ∆rGm − RT ∆ngas = −817897J mol−1−(8.3144J mol−1K−1)(298K)(−2) = −812.941kJ mol−1 = max. work (c) the maximum amount of non-pV work obtainable from the reaction per mole. Answer: ◦ −1 max. non-pV work = ∆rGm = −817.897kJ mol 2. A certain gas obeys the equation of state pVm = RT + βp 1 where β depends only on the temperature. For this gas show that ∂U ! RT 2 dβ ! = 2 ∂V T (Vm − β) dT Answer: ∂U ! ∂p ! = T − p ∂V T ∂T V RT p = Vm − β(T ) ∂p ! R RT dβ = + 2 ∂T V Vm − β (Vm − β) dT Then ∂U ! RT RT 2 dβ = + 2 − p ∂V T Vm − β (Vm − β) dT RT RT 2 dβ RT = + 2 − Vm − β (Vm − β) dT Vm − β RT 2 dβ = 2 (Vm − β) dT 3. Show that ! 2 ! ∂Cp ∂ V = −T 2 ∂p T ∂T p Answer: ∂H ! Cp = ∂T p ! ! ∂Cp ∂ ∂H = ∂p ∂p ∂T T p T ∂ ∂H ! ! ∂T ∂p T p But dH = T dS + V dp ∂H ! ∂S ! = T + V ∂p T ∂p T dG = −SdT + V dp ∂S ! ∂V ! = − ∂p T ∂T p 2 Then ∂H ! ∂V ! = V − T ∂p T ∂T p and ! ! ∂Cp ∂ ∂V = V − T ∂p ∂T ∂T T p p ∂V ! ∂V ! ∂2V ! = − − T 2 ∂T p ∂T p ∂T p ∂2V ! = −T 2 ∂T p 4.
[Show full text]
Thermal Storage and Transport in Colloidal Nanocrystal-Based Materials by Minglu Liu a Dissertation Presented in Partial Fulfil
Thermal Storage and Transport in Colloidal Nanocrystal-Based Materials by Minglu Liu A Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy Approved November 2015 by the Graduate Supervisory Committee: Robert Wang, Chair Liping Wang Konrad Rykaczewski Patrick Phelan Lenore Dai ARIZONA STATE UNIVERSITY December 2015 ABSTRACT The rapid progress of solution-phase synthesis has led colloidal nanocrystals one of the most versatile nanoscale materials, provided opportunities to tailor material's properties, and boosted related technological innovations. Colloidal nanocrystal-based materials have been demonstrated success in a variety of applications, such as LEDs, electronics, solar cells and thermoelectrics. In each of these applications, the thermal transport property plays a big role. An undesirable temperature rise due to inefficient heat dissipation could lead to deleterious effects on devices' performance and lifetime. Hence, the first project is focused on investigating the thermal transport in colloidal nanocrystal solids. This study answers the question that how the molecular structure of nanocrystals affect the thermal transport, and provides insights for future device designs. In particular, PbS nanocrystals is used as a monitoring system, and the core diameter, ligand length and ligand binding group are systematically varied to study the corresponding effect on thermal transport. Next, a fundamental study is presented on the phase stability and solid-liquid transformation of metallic (In, Sn and Bi) colloidal nanocrystals. Although the phase change of nanoparticles has been a long-standing research topic, the melting behavior of colloidal nanocrytstals is largely unexplored. In addition, this study is of practical importance to nanocrystal-based applications that operate at elevated temperatures.
[Show full text]
States of Matter Chemistry 1-2 Enriched Mr
States of Matter Chemistry 1-2 Enriched Mr. Chumbley Modern Chemistry: Chapter 10 THE KINETIC-MOLECULAR THEORY OF MATTER Section 1 p. 310 – 314 Kinetic-Molecular Theory • It is generally not possible to study individual particles, so scientists study the behavior of large groups of particles • The kinetic molecular theory was developed in the late 19th century to account for the different ways matter behaves as a solid, liquid, or gas • The kinetic-molecular theory explains that the behavior of physical systems depends on the combined actions of the molecules constituting the system KMT and Gases • Kinetic-molecular theory can be used to describe the properties and behavior of all states of matter, but is well demonstrated by gases • An ideal gas is a hypothetical gas that perfectly fits all the assumptions of the kinetic-molecular theory Kinetic-Molecular Theory of Gases • Gases consist of large numbers of tiny particles that are far apart relative to their size • Collisions between gas particles and between particles and container walls are elastic collisions • An elastic collision is one in which there is no net loss of kinetic energy • Gas particles are in continuous, rapid, random motion and possess kinetic energy • Kinetic energy is the energy of motion • There are no forces of attraction between gas particles • The temperature of a gas depends on the average kinetic energy of the particles of the gas Properties of Gases • Expansion • Gases do not have a definite shape or volume, but rather completely fill their container • Fluidity
[Show full text]
Measurement of High Temperature Heat Content of Silicon by Drop Calorimetry
Journal of Thermal Analysis and Calorimetry, Vol. 69 (2002) 1059–1066 MEASUREMENT OF HIGH TEMPERATURE HEAT CONTENT OF SILICON BY DROP CALORIMETRY K. Yamaguchi1* and K. Itagaki2 1Department of Materials Science and Technology, Faculty of Engineering, Iwate University, Ueda, Morioka, 020-8551, Japan 2Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Katahira, Aoba-Ku, Sendai, 980-8577, Japan Abstract Heat content of silicon has been measured in a temperature range of 700–1820 K using a drop calo- rimeter. Boron nitride was used as a sample crucible. The enthalpy of fusion and the melting point of silicon determined from the heat content-temperature plots are 48.31±0.18 kJ mol–1 and 1687±5 K, respectively. The heat content and heat capacity equations were derived using the Shomate function for the solid region and the least square method for the liquid region, respectively, and compared with the literature values. Keywords: drop calorimeter, enthalpy of fusion, heat capacity, heat content, high temperature, melting point, silicon Introduction Single crystals of silicon are important materials used in electronic device applica- tions. The solid and liquid phases coexist at the quasi-equilibrium state in conven- tional processes to fabricate the single crystal of silicon. Therefore, knowledge of the thermochemical data such as heat capacity, melting point and enthalpy of fusion is important for the analysis of fabricating processes. Furthermore, production of a sin- gle crystal of silicon having the higher quality and a larger diameter is required for the Czochralski (Cz) technique of single crystal growth. In order to achieve this demand, mathematical simulations of the transport phenomena prevailing in the Cz single crystal growth have been carried out based on the thermochemical data.
[Show full text]